Given the constraints (10 minutes total, 5 minutes for poison to kill), you can also divide the wine into 10 groups and assign each group to each of the 10 mice

Given the constraints (10 minutes total, 5 minutes for poison to kill), you can also divide the wine into 10 groups and assign each group to each of the 10 mice. The mice then drink samples from every bottle in his group, and after 5 minutes, the one that dies has the group with poison in it. You then assign each of the rats a bottle from this group, and then see which one of them dies. If they all live, then the remaining bottle is poisoned. Granted, your solution is better, but you can solve this problem without binary tricks.